#include <FemKernel.hpp>
Public Member Functions | |
| FemKernel (const Grid< fem_types > &grid) | |
| const Grid< fem_types > & | grid () const |
| void | set_element (std::size_t element) |
| void | set_boundary_element (std::size_t boundary_element) |
| void | lazy_set_element (std::size_t element) |
| float_t | shape_value (std::size_t integrator_node, std::size_t element_node) const |
| const ublas::fixed_vector < float_t, fem_types::data_dimension > & | shape_gradient (std::size_t integrator_node, std::size_t element_node) const |
| float_t | transform_determinant (std::size_t integrator_node) const |
| float_t | shape_boundary_value (std::size_t integrator_node, std::size_t element_node) const |
| float_t | shape_boundary_derivative (std::size_t integrator_node, std::size_t element_node) const |
| float_t | boundary_transform_determinant (std::size_t integrator_node) const |
| const ublas::fixed_vector < float_t, fem_types::data_dimension > & | boundary_normal () const |
| std::size_t | current_element () const |
| std::size_t | current_boundary_element () const |
| bool | is_boundary_node (std::size_t element_node) const |
| const ublas::fixed_vector < float_t, fem_types::data_dimension > | boundary_normal_at_node (std::size_t element_node) const |
FemKernel is a class which is used to evaluate functions in the integration nodes on a given element. The integrator, the shape function and the element type is specified by the template parameter fem_types. If a FemKernel is set to an element by calling set_element() or set_boundary_element(), it precomputes the values and derivatives of the shape functions and the element transformation in the integration points. Then you can use the accessor functions to query these values.
A FemKernel object is automatically created by Assembler::assemble(), Assembler::assemble_stiffness_matrix() or Assembler::assemble_force_vector() and then iteratively set to the elements in a given grid during the assembly process. The initialized kernel is then passed to the equation object of the current FE computation. In the implementation of the equation (cf. EquationInterface) you can query the kernel to compute the equation coefficients which you then pass back to the assembly function.
| imaging::FemKernel< fem_types >::FemKernel | ( | const Grid< fem_types > & | grid | ) | [inline] |
Construct kernel from grid. The kernel object stores only a reference to the grid. When the kernel is later on set to an element by calling void set_element(std::size_t element) or set_boundary_element(std::size_t element) the argument element refers to grid.
| const Grid<fem_types>& imaging::FemKernel< fem_types >::grid | ( | ) | const [inline] |
Returns a reference to the grid, which was passed to kernel during construction. The kernel object stores only a reference to the grid.
Referenced by imaging::TvFlowStep< fem_types >::force_vector(), imaging::PoissonEquation< fem_types >::force_vector(), imaging::McmStep< fem_types >::force_vector(), imaging::GeodesicActiveContourStep< fem_types >::force_vector(), imaging::DiffusionStep< fem_types >::force_vector(), imaging::PoissonEquation< fem_types >::force_vector_at_boundary(), imaging::TvFlowStep< fem_types >::sanity_check_force_vector(), imaging::PoissonEquation< fem_types >::sanity_check_force_vector(), imaging::McmStep< fem_types >::sanity_check_force_vector(), imaging::GeodesicActiveContourStep< fem_types >::sanity_check_force_vector(), imaging::DiffusionStep< fem_types >::sanity_check_force_vector(), imaging::TvFlowStep< fem_types >::sanity_check_stiffness_matrix(), imaging::McmStep< fem_types >::sanity_check_stiffness_matrix(), imaging::GeodesicActiveContourStep< fem_types >::sanity_check_stiffness_matrix(), imaging::DiffusionStep< fem_types >::sanity_check_stiffness_matrix(), imaging::TvFlowStep< fem_types >::stiffness_matrix(), imaging::McmStep< fem_types >::stiffness_matrix(), imaging::GeodesicActiveContourStep< fem_types >::stiffness_matrix(), and imaging::DiffusionStep< fem_types >::stiffness_matrix().
| void imaging::FemKernel< fem_types >::set_element | ( | std::size_t | element | ) | [inline] |
Initializes the kernel to element, computes
References imaging::inverse().
Referenced by imaging::Assembler::assemble(), imaging::Assembler::assemble_force_vector(), imaging::Assembler::assemble_stiffness_matrix(), imaging::average(), imaging::integrate(), imaging::maximum(), and imaging::minimum().
| void imaging::FemKernel< fem_types >::set_boundary_element | ( | std::size_t | boundary_element | ) | [inline] |
Initializes the kernel to boundary_element, computes
References imaging::FemKernel< fem_types >::boundary_normal(), and imaging::inverse().
Referenced by imaging::Assembler::assemble(), imaging::Assembler::assemble_force_vector(), and imaging::Assembler::assemble_stiffness_matrix().
| void imaging::FemKernel< fem_types >::lazy_set_element | ( | std::size_t | element | ) | [inline] |
Initializes the kernel to element, but does not compute new values of the shape and transformation functions. Use this function if you know for sure that the geometry of the new element is exactly the same as the one of the previous element. As long as set_element() or lazy_set_element() are not called with a different parameter element, current_element() will return element.
Referenced by imaging::Assembler::assemble(), imaging::Assembler::assemble_force_vector(), imaging::Assembler::assemble_stiffness_matrix(), imaging::average(), imaging::integrate(), imaging::maximum(), and imaging::minimum().
| float_t imaging::FemKernel< fem_types >::shape_value | ( | std::size_t | integrator_node, | |
| std::size_t | element_node | |||
| ) | const [inline] |
Returns the value of the shape function assciated with element_node in the integration node integrator_node.
Referenced by imaging::SimpleEquationAdaptor< equation_t >::force_vector(), imaging::Grid< fem_types >::interpolate_value(), and imaging::SimpleEquationAdaptor< equation_t >::stiffness_matrix().
| const ublas::fixed_vector<float_t, fem_types::data_dimension>& imaging::FemKernel< fem_types >::shape_gradient | ( | std::size_t | integrator_node, | |
| std::size_t | element_node | |||
| ) | const [inline] |
Returns the gradient of the shape function assciated with element_node in the integration node integrator_node.
Referenced by imaging::SimpleEquationAdaptor< equation_t >::force_vector(), imaging::Grid< fem_types >::interpolate_gradient(), and imaging::SimpleEquationAdaptor< equation_t >::stiffness_matrix().
| float_t imaging::FemKernel< fem_types >::transform_determinant | ( | std::size_t | integrator_node | ) | const [inline] |
Returns the value of the transformation determinant (determinant of the Jacobian of the transform) in the integration node integrator_node. This value reflects the distortion of the actual element with respect to its reference element. Note that integrator_node refers to the corresponding node of the boundary integrator.
Referenced by imaging::Assembler::assemble(), imaging::Assembler::assemble_force_vector(), imaging::Assembler::assemble_stiffness_matrix(), imaging::average(), and imaging::integrate().
| float_t imaging::FemKernel< fem_types >::shape_boundary_value | ( | std::size_t | integrator_node, | |
| std::size_t | element_node | |||
| ) | const [inline] |
Returns the value of shape function associated with element_node on the parent element of the current boundary element in the integration node integrator_node on the boundary element. This means that the shape function on the element is evaluated at the boundary of the element. Keep in mind that here the element is not the current element but the parent element of the current boundary element. I.e. this function depends only on the current boundary element. Note that integrator_node refers to the corresponding node of the boundary integrator.
Referenced by imaging::SimpleEquationAdaptor< equation_t >::force_vector_at_boundary(), imaging::Grid< fem_types >::interpolate_boundary_value(), and imaging::SimpleEquationAdaptor< equation_t >::stiffness_matrix_at_boundary().
| float_t imaging::FemKernel< fem_types >::shape_boundary_derivative | ( | std::size_t | integrator_node, | |
| std::size_t | element_node | |||
| ) | const [inline] |
Returns the gradient of shape function associated with element_node on the parent element of the current boundary element in the integration node integrator_node on the boundary element. This means that the gradient of the shape function on the element is evaluated at the boundary of the element. Keep in mind that here the element is not the current element but the parent element of the current boundary element. I.e. this function depends only on the current boundary element. Note that integrator_node refers to the corresponding node of the boundary integrator.
Referenced by imaging::Grid< fem_types >::interpolate_boundary_derivative(), and imaging::SimpleEquationAdaptor< equation_t >::stiffness_matrix_at_boundary().
| float_t imaging::FemKernel< fem_types >::boundary_transform_determinant | ( | std::size_t | integrator_node | ) | const [inline] |
Returns the value of the transformation determinant (determinant of the Jacobian of the transform) of the transformation which transforms the current boundary element to the reference element. This value reflects the distortion of the actual boundary element with respect to its reference element.
Referenced by imaging::Assembler::assemble(), imaging::Assembler::assemble_force_vector(), imaging::Assembler::assemble_stiffness_matrix(), and imaging::SimpleEquationAdaptor< equation_t >::stiffness_matrix_at_boundary().
| const ublas::fixed_vector<float_t, fem_types::data_dimension>& imaging::FemKernel< fem_types >::boundary_normal | ( | ) | const [inline] |
Returns the boundary normal in the integration node integrator_node of the current boundary element. Note that integrator_node refers to the corresponding node of the boundary integrator.
Referenced by imaging::FemKernel< fem_types >::set_boundary_element().
| std::size_t imaging::FemKernel< fem_types >::current_element | ( | ) | const [inline] |
Returns the index of the current element. In most situations you should assume that the kernel is initialized to this element.
Referenced by imaging::Grid< fem_types >::global_coordinates(), imaging::Grid< fem_types >::interpolate_gradient(), and imaging::Grid< fem_types >::interpolate_value().
| std::size_t imaging::FemKernel< fem_types >::current_boundary_element | ( | ) | const [inline] |
Returns the index of the current boundary element. In most situations you should assume that the kernel is initialized to this boundary element.
Referenced by imaging::Grid< fem_types >::interpolate_boundary_derivative(), and imaging::Grid< fem_types >::interpolate_boundary_value().
| bool imaging::FemKernel< fem_types >::is_boundary_node | ( | std::size_t | element_node | ) | const [inline] |
Returns true if element_node refers to a node index on the reference element which lies at the boundary of the grid in the current element.
Referenced by imaging::SimpleEquationAdaptor< equation_t >::force_vector(), and imaging::SimpleEquationAdaptor< equation_t >::stiffness_matrix().
| const ublas::fixed_vector<float_t, fem_types::data_dimension> imaging::FemKernel< fem_types >::boundary_normal_at_node | ( | std::size_t | element_node | ) | const [inline] |
Returns the boundary normal in element_node of the current element. The parameter element_node refers to the index of the node as in the reference element.
1.5.5